Quantum space-time marginal problem: global causal structure from local causal information
Spatial and temporal quantum correlations can be unified in the framework of the pseudo-density operators (PDOs), and quantum causality between the involved events in an experiment is encoded in the corresponding PDO. We study the relationship between local causal information and global causal struc...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2023-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/ad1416 |
| _version_ | 1797383216582098944 |
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| author | Zhian Jia Minjeong Song Dagomir Kaszlikowski |
| author_facet | Zhian Jia Minjeong Song Dagomir Kaszlikowski |
| author_sort | Zhian Jia |
| collection | DOAJ |
| description | Spatial and temporal quantum correlations can be unified in the framework of the pseudo-density operators (PDOs), and quantum causality between the involved events in an experiment is encoded in the corresponding PDO. We study the relationship between local causal information and global causal structure. A space-time marginal problem is proposed to infer global causal structures from given marginal causal structures where causal structures are represented by the reduced PDOs; we show that there almost always exists a solution in this case. By imposing the corresponding constraints on this solution set, we could obtain the required solutions for special classes of marginal problems, like a positive semidefinite marginal problem, separable marginal problem, etc. We introduce a space-time entropy and propose a method to determine the global causal structure based on the maximum entropy principle. The notion of quantum pseudo-channel (QPC) is also introduced and we demonstrate that the QPC marginal problem can be solved by transforming it into a PDO marginal problem via the channel-state duality. |
| first_indexed | 2024-03-08T21:17:37Z |
| format | Article |
| id | doaj.art-a747d3199adf45cfb37eddf13f147853 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-08T21:17:37Z |
| publishDate | 2023-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-a747d3199adf45cfb37eddf13f1478532023-12-21T14:22:29ZengIOP PublishingNew Journal of Physics1367-26302023-01-01251212303810.1088/1367-2630/ad1416Quantum space-time marginal problem: global causal structure from local causal informationZhian Jia0https://orcid.org/0000-0001-8588-173XMinjeong Song1Dagomir Kaszlikowski2Centre for Quantum Technologies, National University of Singapore , Singapore 117543, Singapore; Department of Physics, National University of Singapore , Singapore 117543, SingaporeNanyang Quantum Hub, School of Physical and Mathematical Sciences, Nanyang Technological University , Singapore 637371, SingaporeCentre for Quantum Technologies, National University of Singapore , Singapore 117543, Singapore; Department of Physics, National University of Singapore , Singapore 117543, SingaporeSpatial and temporal quantum correlations can be unified in the framework of the pseudo-density operators (PDOs), and quantum causality between the involved events in an experiment is encoded in the corresponding PDO. We study the relationship between local causal information and global causal structure. A space-time marginal problem is proposed to infer global causal structures from given marginal causal structures where causal structures are represented by the reduced PDOs; we show that there almost always exists a solution in this case. By imposing the corresponding constraints on this solution set, we could obtain the required solutions for special classes of marginal problems, like a positive semidefinite marginal problem, separable marginal problem, etc. We introduce a space-time entropy and propose a method to determine the global causal structure based on the maximum entropy principle. The notion of quantum pseudo-channel (QPC) is also introduced and we demonstrate that the QPC marginal problem can be solved by transforming it into a PDO marginal problem via the channel-state duality.https://doi.org/10.1088/1367-2630/ad1416temporal quantum correlationquantum marginal problempseudo-density operatorchannel marginal problemquantum causalitymaximum entropy principle |
| spellingShingle | Zhian Jia Minjeong Song Dagomir Kaszlikowski Quantum space-time marginal problem: global causal structure from local causal information New Journal of Physics temporal quantum correlation quantum marginal problem pseudo-density operator channel marginal problem quantum causality maximum entropy principle |
| title | Quantum space-time marginal problem: global causal structure from local causal information |
| title_full | Quantum space-time marginal problem: global causal structure from local causal information |
| title_fullStr | Quantum space-time marginal problem: global causal structure from local causal information |
| title_full_unstemmed | Quantum space-time marginal problem: global causal structure from local causal information |
| title_short | Quantum space-time marginal problem: global causal structure from local causal information |
| title_sort | quantum space time marginal problem global causal structure from local causal information |
| topic | temporal quantum correlation quantum marginal problem pseudo-density operator channel marginal problem quantum causality maximum entropy principle |
| url | https://doi.org/10.1088/1367-2630/ad1416 |
| work_keys_str_mv | AT zhianjia quantumspacetimemarginalproblemglobalcausalstructurefromlocalcausalinformation AT minjeongsong quantumspacetimemarginalproblemglobalcausalstructurefromlocalcausalinformation AT dagomirkaszlikowski quantumspacetimemarginalproblemglobalcausalstructurefromlocalcausalinformation |